Non-Bloch band theory of nonlinear eigenvalue problems

Kota Otsuka; Kazuki Yokomizo

Home/Archive/arXiv

arXiv · 2604.24284

Non-Bloch band theory of nonlinear eigenvalue problems

Kota Otsuka·Kazuki Yokomizo

View original source ↗Read source document ↗Export metadata ↓

Abstract

Nonlinear eigenvalue problems arise in a wide range of physical systems, in which system parameters depend on the eigenvalue. Such systems have been proposed to exhibit an extreme sensitivity of their spectra to boundary conditions, which leads to the breakdown of conventional topological characterizations. In this work, we establish a non-Bloch framework for calculating continuum bands that reproduce the spectra of the nonlinear system with open boundary conditions. This non-Bloch band theory enables us not only to calculate the eigenvalues but also to reveal phenomena unique to the nonlinear system. We further investigate the topological bulk-boundary correspondence in a nonlinear Chern insulator within an extended version of this framework.

Explore related subjects

cond-mat.mes-hall

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Kota Otsuka, Kazuki Yokomizo. 2026-04-27. Non-Bloch band theory of nonlinear eigenvalue problems. https://arxiv.org/abs/2604.24284

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Non-Markovian Quantum Dynamics of Exciton-Polaritons

Exciton-polaritons, hybrid light-matter quasiparticles formed when a material interacts with a confined electric field, have experimentally been shown to exhibit mesoscale coherent quantum propagation that remains robust at room temperature. However, an accurate and direct quantum dynamical simulation of this phenomenon that does not resort to semi-classical approximations is prohibitively expensive computationally, limiting the microscopic understanding of the rich dynamical interplay among phonons, photons, and electrons under collective light-matter coupling. To address this fundamental challenge, we develop a non-Markovian master equation approach which enables the fully quantum mechanical simulation of non-equilibrium exciton-polariton dynamics and captures phonon-induced decoherence and dissipation beyond the conventional Markovian limit. To carry out this task, a procedure is developed in which the wave vector space is coarse-grained and each diagonal element of the density matrix is evolved in parallel. To demonstrate the utility of this approach, we simulate exciton-polariton transport in TIPS-pentacene. We find that our approach reasonably captures the experimentally observed renormalization of the polariton group velocity, which originates from the phonon-induced non-Markovian Lamb shift. We further show that this renormalization cannot be reproduced within conventional Markovian theories.

cond-mat.mes-hall↗

arXiv2026

Long-range spin-polarized Josephson effect in ballistic S/F/S junctions with precessing magnetization

We present a theory of ballistic N/F/S and S/F/S junctions with a uniformly precessing magnetization, which generates long-range equal-spin superconducting correlations [Takahashi et al., Phys. Rev. Lett. 99, 057003 (2007), Houzet, Phys. Rev. Lett. 101, 057009 (2008)]. The non-equilibrium distribution of Andreev bound states leads to a strongly non-sinusoidal current-phase relationship for large precession angles. We derive detailed results for ballistic junctions involving partially and fully polarized ferromagnets. In the fully polarized half-metal limit, the magnetization precession switches the junction from an "off" state with vanishing subgap current to an "on" state with finite Andreev conductance and finite Josephson current.

cond-mat.mes-hall↗

arXiv2026

Super-resolution Control of Individual Two-dimensional Quantum Emitters

Localized interlayer excitons in semiconducting transition-metal dichalcogenide heterobilayers are quantum emitters with a static electric dipole moment, making them excellent nanoscale charge sensors to probe correlated quantum phases in a proximal layer. These emitters are electrically tunable and inherit spin-valley selection rules, yet their deterministic spatial control remains challenging due to subwavelength confinement. Here, we present a platform that combines cryogenic optical spectroscopy with scanning probe microscopy to investigate trapped interlayer excitons in MoSe$_2$/WSe$_2$ bilayers. By exploiting tip-induced local Stark shift, we achieve super-resolution of emitters separated by a few tens of nanometers and demonstrate deterministic control of individual charge states, including trion formation. Time-resolved measurements reveal tip-induced modification of the electromagnetic vacuum around individual emitters, and thus control of their radiative emission. Our multi-point charge sensing platform with optical readout is particularly well-suited for future study of fractionalization and anyon dynamics in semiconducting fractional Chern insulators.

cond-mat.mes-hall↗